Dielectric constant medium effects

The most water-like of this class of solvents is methanol, for it maintains much the same nice balance of basic and acidic properties found in water. Its autoprotolysis constant is smaller than that of water (Table 3.3.4) because of its lower dielectric constant. Medium effects for transfer of ionisation equilibria from water to methanol are approximately constant for closely related acids. For six cation acids, the pyri-dinium ion and five methyl derivatives, the average medium ejffect is 0.06 0.02, small because the ionisation of these cations creates no new charge field. For phenol and thirteen of its derivatives the medium effect is 4.32 0.09 smaller values are obtained for nitrophenols, possibly because the anions are stabilised by dispersion interactions with methanol. For 23 carboxylic acids, aliphatic and aromatic, the average medium effect is 4.87 0.15. Values of the medium effect for individual acids are collected in Appendix 3.5.5. 

Continuum solvation models are generally focused on purely electrostatic effects the solvent is a homogeneous continuous medium and its response is determined by its dielectric constant. Electrostatic effects usually constitute the dominating part of the solute - solvent interaction but in some cases explicit solute-solvent (or solute-solute)... 

As a rule, the presence of a high dielectric constant medium leads to the rise of the dipole moment of the compound. However, the relative increase of the dipole moment varies substantially from one structure to another. For instance, the calculated dipole moment of 2(H)-3-pyrazolone (7) increases by 72% when transferred from the medium with e = 1 to the medium with s = 80, whereas the corresponding change in the dipole moment of pyrazole (3) is only 15%. Therefore, it is questionable to assume constant dipole moment values for a series of congeneric compounds in different dielectric media and derive correlations of the chemical reactivity or physical properties of such series of compounds with some fixed function of the dielectric constant of the solvent (a common approach in the linear free energy relationship studies of solvent effects, cf. [65-67]). 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

The angles ot, p, and x relate to the orientation of the dipole nionient vectors. The geonieti y of interaction between two bonds is given in Fig. 4-16, where r is the distance between the centers of the bonds. It is noteworthy that only the bond moments need be read in for the calculation because all geometr ic features (angles, etc.) can be calculated from the atomic coordinates. A default value of 1.0 for dielectric constant of the medium would normally be expected for calculating str uctures of isolated molecules in a vacuum, but the actual default value has been increased 1.5 to account for some intramolecular dipole moment interaction. A dielectric constant other than the default value can be entered for calculations in which the presence of solvent molecules is assumed, but it is not a simple matter to know what the effective dipole moment of the solvent molecules actually is in the immediate vicinity of the solute molecule. It is probably wrong to assume that the effective dipole moment is the same as it is in the bulk pure solvent. The molecular dipole moment (File 4-3) is the vector sum of the individual dipole moments within the molecule. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

Solvent Effects on the Rate of Substitution by the S l Mechanism Table 8 6 lists the relative rate of solvolysis of tert butyl chloride m several media m order of increasing dielectric constant (e) Dielectric constant is a measure of the ability of a material m this case the solvent to moderate the force of attraction between oppositely charged par tides compared with that of a standard The standard dielectric is a vacuum which is assigned a value e of exactly 1 The higher the dielectric constant e the better the medium is able to support separated positively and negatively charged species 8olvents... 

The dielectric constant of the medium affects the equilibria where charges are generated in the dissociations e.g. AH A -I- H" " and therefore affects the pK values. However, its effect on dissociations where there are no changes in total charge such as BH B -1- H" " is considerably less, with a slight decrease in pK with decreasing dielecuic constant. 

The magnitude of the anomeric effect depends on the nature of the substituent and decreases with increasing dielectric constant of the medium. The effect of the substituent can be seen by comparing the related 2-chloro- and 2-methoxy-substituted tetrahydropy-rans in entries 2 apd 3. The 2-chloro compound exhibits a significantly greater preference for the axial orientation than the 2-methoxy compound. Entry 3 also provides data relative to the effect of solvent polarity it is observed that the equilibrium constant is larger in carbon tetrachloride (e = 2.2) than in acetonitrile (e = 37.5). 

It should be noted that, if the medium between the particle and substrate is something other than vacuum and possesses a dielectric constant e, the interaction energy in Eq. 68 is reduced by a factor of Eq. 68, which relates the interaction energy between permanent electric dipoles and their separation distances is known as the Keesom effect. 

To go from experimental observations of solvent effects to an understanding of them requires a conceptual basis that, in one approach, is provided by physical models such as theories of molecular structure or of the liquid state. As a very simple example consider the electrostatic potential energy of a system consisting of two ions of charges Za and Zb in a medium of dielectric constant e. 

Ultimately physical theories should be expressed in quantitative terms for testing and use, but because of the eomplexity of liquid systems this can only be accomplished by making severe approximations. For example, it is often neeessary to treat the solvent as a continuous homogeneous medium eharaeterized by bulk properties such as dielectric constant and density, whereas we know that the solvent is a molecular assemblage with short-range structure. This is the basis of the current inability of physical theories to account satisfactorily for the full scope of solvent effects on rates, although they certainly can provide valuable insights and they undoubtedly capture some of the essential features and even cause-effect relationships in solution kinetics. Section 8.3 discusses physical theories in more detail. 

If we now transfer our two interacting particles from the vacuum (whose dielectric constant is unity by definition) to a hypothetical continuous isotropic medium of dielectric constant e > 1, the electrostatic attractive forces will be attenuated because of the medium s capability of separating charge. Quantitative theories of this effect tend to be approximate, in part because the medium is not a structureless continuum and also because the bulk dielectric constant may be an inappropriate measure on the molecular scale. Eurther discussion of the influence of dielectric constant is given in Section 8.3. 

Sn2 reactions with anionic nucleophiles fall into this class, and observations are generally in accord with the qualitative prediction. Unusual effects may be seen in solvents of low dielectric constant where ion pairing is extensive, and we have already commented on the enhanced nucleophilic reactivity of anionic nucleophiles in dipolar aprotic solvents owing to their relative desolvation in these solvents. Another important class of ion-molecule reaction is the hydroxide-catalyzed hydrolysis of neutral esters and amides. Because these reactions are carried out in hydroxy lie solvents, the general medium effect is confounded with the acid-base equilibria of the mixed solvent lyate species. (This same problem occurs with Sn2 reactions in hydroxylic solvents.) This equilibrium is established in alcohol-water mixtures ... 

The simplest reaction field model is a spherical cavity, where only the net charge and dipole moment of the molecule are taken into account, and cavity/dispersion effects are neglected. For a net charge in a cavity of radius a, the difference in energy between vacuum and a medium with a dielectric constant of e is given by the Bom model. ... 

Some recent studies have underlined the effect that certain physical properties of the reaction medium have in governing the nature and yields of the products obtained when indole Grignard reagents react with alkyl or alkynyl halides. Such factors include the basicity and dielectric constant of the medium and its ability to solvate any of the reacting species. ... 

There have been numerous studies on the kinetics of decomposition of A IRK. AIBMe and other dialkyldiazenes.46 Solvent effects on are small by conventional standards but, nonetheless, significant. Data for AIBMe is presented in Table 3.3. The data come from a variety of sources and can be seen to increase in the series where the solvent is aliphatic < ester (including MMA) < aromatic (including styrene) < alcohol. There is a factor of two difference between kA in methanol and k< in ethyl acetate. The value of kA for AIBN is also reported to be higher in aromatic than in hydrocarbon solvents and to increase with the dielectric constant of the medium.31 79 80 Tlic kA of AIBMe and AIBN show no direct correlation with solvent viscosity (see also 3.3.1.1.3), which is consistent with the reaction being irreversible (Le. no cage return). 

This is a reaction in which neutral molecules react to give a dipolar or ionic transition state, and some rate acceleration from the added neutral salt is to be expected53, since the added salt will increase the polarity or effective dielectric constant of the medium. Some of the rate increases due to added neutral salts are attributable to this cause, but it is doubtful that they are all thus explained. The set of data for constant initial chloride and initial salt concentrations and variable initial amine concentrations affords some insight into this aspect of the problem. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

---